Homework # 3. Chapter 38. Photons, Electrons & Atoms

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1 Homwork # 3 Chaptr 38 Photos, Elctros & Atoms

2 38.4 A lasr usd to wld dtachd rtias mits light with a wavlgth of 650 m i pulss that ar 25.0 ms i duratio. Th avrag powr durig ach puls is 0.6 W. (a) How much rgy is i ach puls i jouls? (b) How much rgy is i ach puls i lctro volts? (c) What is th rgy of o photo i jouls? (d) What is th rgy of o photo i lctro volts? () How may photos ar i ach puls? (a) E P t (0.6 W)(25 ms) 15 mj (b) 15 x 10-3 J (1 V/1.6 x J) 9.4 x V (c) E hf hc/λ (2 x J-m)/(650 x 10-9 m) 3.06 x J (d) E hf hc/λ (1.24 V-µm)/(0.650 µm) 1.91 V () # of photos total rgy/rgy pr photo N 15 mj / (3.06 x J) 4.9 x photos hc (6.63 x J-s)(3 x 10 8 m/s) 2 x J-m 1.24 V-µm

3 38.7 A cla ickl surfac is xposd to light with a wavlgth of 209 m. Th photolctric work fuctios for ickl is 5.10 V. What is th maximum spd of th photolctros mittd from this surfac? Us m/s for th spd of light i a vacuum, J-s for Plack's costat, ad Kg for th mass of a lctro. KE hf φ hc/λ φ (1.24 V-µm)/(0.209 µm) 5.10 V 0.83 V 0.83 V (1.6 x J/V) 13.3 x J KE ½ mv x ½ (9.11 x )v 2 v 5.4 x 10 5 m/s

4 38.12 Th photolctric work fuctio of potassium is 2.3 V. Light havig a wavlgth of 260 m falls o potassium. (a) Fid th stoppig pottial for light of this wavlgth. (b) Fid th kitic rgy of th most rgtic lctros jctd. (c) Fid th spds of ths lctros. (a) KE hf φ hc/λ φ (1.24 V-µm)/(0.260 µm) 2.3 V 2.47 V stoppig pottial V o KE max 2.25 V (b) KE 2.47 V (c) 2.47 V (1.6 x J/V) 3.95 x J KE ½ mv x ½ (9.11 x )v 2 v 9.3 x 10 5 m/s

5 38.20 A 4.87-MV alpha particl from a radium 226 Ra dcay maks a hado collisio with a uraium uclus. A uraium uclus has 92 protos. (a) What is th distac of closst approach of th alpha particl to th ctr of th uclus? Assum that th uraium uclus rmais at rst ad that th distac of closst approach is much largr tha th radius of th uraium uclus. (b) What is th forc o th alpha particl at th istat wh it is at th distac of closst approach? (a) U(r) k q 1 q 2 /r KE (9 x 10 9 ) (2)(92)(1.6 x ) 2 / r (4.87 x 10 6 V)(1.6 x J/V) r 5.44 x m (b) F k q 1 q 2 /r 2 U/r F (4.87 x 10 6 V)(1.6 x J/V)/(5.44 x m) F 14.3 N

6 38.31 A larg umbr of o atoms ar i thrmal quilibrium. (a) What is th ratio of th umbr of atoms i a stat to th umbr i a 3p stat at 260 K? (b) What is th ratio of th umbr of atoms i a stat to th umbr i a 3p stat at 520 K? (c) What is th ratio of th umbr of atoms i a stat to th umbr i a 3p stat at 1000 K? Th rgis of ths stats ar show i Fig.38.24a i th txtbook. (d) At ay of ths tmpraturs, th rat at which a o gas will spotaously mit mm radiatio is quit low. Explai why. E (a) (b) (c) 3 p ( E E ) / kt 3 p From Fig.38.24a i th txtbook E V ad E V 3 p E3 p V V 1.96 V( J/1 V) J 3p 3p 3p ( ( ( J)/( J)/( J)/( J / K)(260K) J / K)(520K) J / K)(1000K) (d) At ach of ths tmpraturs th umbr of atoms i th xcitd stat, th iitial stat for th trasitio that mits m radiatio, is quit small. Th ratio icrass as th tmpratur icrass.

7 38.37 X-rays with iitial wavlgth m udrgo Compto scattrig. (a) What is th largst wavlgth foud i th scattrd X-rays? (b) At which scattrig agl is this wavlgth obsrvd? Solv for h λ λ (1 cos φ) λc (1 cos φ) mc λ : λ λ + λ (1 cos φ) (b) Th largst λ corrspods to φ 180 o. C (a) λ λ + λ C m 2( m) m m.

8 38.40 A photo scattrs i th backward dirctio (θ 180 o ) from a fr proto that is iitially at rst. What must th wavlgth of th icidt photo b if it is to udrgo a 10.0% chag i wavlgth as a rsult of th scattrig? λ λ h h (1 cos φ) λ (1 cos φ). mcλ λ mc λ 34 ( J s) 14 λ (1 + 1) m ( kg)( m/s)(0.100)

9 38.54 (a) If th avrag frqucy mittd by a 200 W light bulb is 5 x Hz, ad 10.0% of th iput powr is mittd as visibl light, approximatly how may visibl-light photos ar mittd pr scod? (b) At what distac would this corrspod to visibl-light photos pr squar ctimtr pr scod if th light is mittd uiformly i all dirctios? (a) dn ( de dt) P (200 W)(0.10) 14 dt ( de dn) hf h( Hz) photos sc. Thrfor, ( dn dt) 4π r photos sc cm. (b) r photos sc 6930 cm 69.3 m π ( photos sc cm ) 1/ 2

10 38.61 A icidt x-ray photo with a wavlgth of m is scattrd i th backward dirctio from a fr lctro that is iitially at rst. (a) What is th magitud of th momtum of th scattrd photo? (b) What is th kitic rgy of th lctro aftr th photo is scattrd? (a) Th wavlgth of th scattrd photo is giv by th Compto shift: h λ λ + (1 cos φ) mc with φ 180 o so λ λ + 2h/mc λ + 2hc/mc m Th momtum of th scattrd photo is p h/λ 6.77 x kg-m/s (b) Apply cosrvatio of rgy to th collisio to calculat th kitic rgy of th lctro aftr th scattrig. Th rgy of th photo is giv by Eq.(38.2), E E + E ; hc / λ hc / λ + E E hc/λ hc/λ hc(1/λ 1/λ ) (1.24 V-µm)[1/(9.3 x ) 1/(9.79 x )] 670 V Th rgy of th icidt photo is 13.8 kv, so oly about 5% of its rgy is trasfrrd to th lctro. This corrspods to a fractioal shift i th photo s wavlgth that is also 5%.

11 38.65 A sampl of hydrog atoms is irradiatd with light with a wavlgth of 85.4 m, ad lctros ar obsrvd lavig th gas. (a) If ach hydrog atom wr iitially i its groud lvl, what would b th maximum kitic rgy i lctro volts of ths photolctros? (b) A fw lctros ar dtctd with rgis as much as 10.2 V gratr tha th maximum kitic rgy calculatd i part (a). How ca this b? (a) (b) hf E E, f i 34 8 hc λ hc λ ( J s)( m/s) m J(1 V/ J) V. Ef Ei + hf. groud stat E i V. E f V V 0.90 V V/ V, 10.2 V gratr tha th rgy of th groud stat. If a lctro with E 3.40 V gais 14.5 V from th absorbd photo, it will d up with 14.5 V 3.4 V 11.1 V of kitic rgy which is 10.2 V gratr tha 0.90 V.

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